Finite Group Databasebeta

← #28400776

Subgroups — #28400776

Order 14464.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299201C211yesmaximal, characteristic, complemented
2#20299079C211yesmaximal, characteristic, complemented
3#20298916C211yesmaximal, characteristic, complemented
4#20298904C211yesmaximal, characteristic, complemented
5#20298901C211yesmaximal, characteristic, complemented
6#20298797C211yesmaximal, characteristic, complemented
7#20298792C211yesmaximal, characteristic, complemented
8#20298745C211yesmaximal, characteristic, complemented
9#20298741C211yesmaximal, characteristic, complemented
10#20298707C211yesmaximal, characteristic, complemented
11#20298697C211yesmaximal, characteristic, complemented
12#20298689C211yesmaximal, characteristic, complemented
13#20298680C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#480×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×D904C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21#16813618C2211yescharacteristic
22#16813613C2211yescharacteristic
23#16813606—21no—
24#16813604—21no—
25#16813596C2211yescharacteristic
26#16813594—21no—
27#16813593—21no—
28#16813587C2211yescharacteristic
29#16813587C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31#16813584C2211yescharacteristic
32#16813584C2211yescharacteristic
33#16813584C2211yescharacteristic
34C4×C22⋊D113—21no—
35C4×C22⋊D113—21no—
36#16813581C2211yescharacteristic
37#16813580—21no—
38C4⋊C4×D113—21no—
39#16813553C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52#121×C113C2211yescharacteristic
53C2×C4⋊C4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—22no—
61C2×Dic226C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C22×Dic113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73#14268636—22no—
74#14268635—22no—
75D904—22no—
76#14268632—22no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113D411yescharacteristic
81C4⋊Dic113D411yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113D411yescharacteristic
88C22⋊Dic113D411yescharacteristic
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100C22×C4×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113—21no—
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110C22×D113—21no—
111C22×D113—21no—
112D4×C113—21no—
113D4×C113—21no—
114D4×C113—81no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—81no—
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2411yescharacteristic
123C22⋊D113—24no—
124C22⋊D113—81no—
125C22⋊D113—81no—
126C22⋊D113—81no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—81no—
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134D452—21no—
135D452—21no—
136D452—21no—
137D452#4112yes—
138C4×D113—24no—
139C4×D113—81no—
140C4×D113—81no—
141C4×D113—81no—
142Dic226—21no—
143Dic226#4112yes—
144C8×C113—21no—
145C8×C113—21no—
146#11744751—21no—
147#11744751—21no—
148C22×C113—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113C22×D411yescharacteristic
155C2×D113—22no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C4×C113—21no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113C2×#4111yescharacteristic
166C4×C113C2×#4111yescharacteristic
167Dic113—22no—
168Dic113—21no—
169Dic113—21no—
170Dic113—21no—
171Dic113—21no—
172Dic113—41no—
173C2×C113—41no—
174C2×C113—81no—
175C2×C113#52511yescharacteristic
176C2×C113#57611yescharacteristic
177C2×C113#57711yescharacteristic
178D113—42no—
179D113—81no—
180#3119—1131nomaximal, Sylow
181C113#311911yescharacteristic, complemented, Sylow
182#540—1131no—
183#520—1131no—
184#481—1131no—
185#480D11311yescharacteristic, complemented
186#479—1131no—
187#478—1131no—
188#460—1131no—
189#459—1131no—
190#449—1131no—
191#449—1131no—
192#442—1131no—
193#440—1131no—
194C4×SD16—1131no—
195C4×D8—1131no—
196#433—1131no—
197C2×#41—1131no—
198C2×SD16—1131no—
199C2×SD16—1131no—
200C2×D8—1131no—
201C2×D8—1131no—
202#127—1131no—
203#125—1131no—
204#123—2261no—
205#123—2261no—
206#121—1131no—
207#121—2261no—
208#121—2261no—
209#121C2×D11311yescharacteristic
210C4×Q8—1131no—
211C4×Q8—1131no—
212C4×D4—1131no—
213C4×D4—1131no—
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—2261no—
217C4×D4—2261no—
218#117—1131no—
219#117—2261no—
220C2×C4⋊C4—2261no—
221C2×C4⋊C4C2×D11311yescharacteristic
222#107C2×D11311yescharacteristic
223#107C2×D11311yescharacteristic
224#106—1131no—
225#106—1131no—
226C4⋊C8—1131no—
227C4⋊C8—1131no—
228#103—1131no—
229#103—1131no—
230#102—1131no—
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102C2×D11311yescharacteristic
235#102C2×D11311yescharacteristic
236C22⋊C8—1131no—
237C22⋊C8C2×D11311yescharacteristic
238#97—1131no—
239C4×C8—1131no—
240#41—2262no—
241#41—2262no—
242C2×Q8—1131no—
243C2×D4—21no—
244C2×D4—1131no—
245C2×D4—1131no—
246C2×D4—2261no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4—2261no—
250C2×D4C22×D11311yescharacteristic
251C22×C4—21no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4C22×D11311yescharacteristic
258SD16—2262no—
259SD16—2262no—
260D8—2262no—
261D8—2262no—
262C2×C8—1131no—
263C2×C8—1131no—
264C2×C8C22×D11311yescharacteristic
265C2×C8C22×D11311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4C22×D11311yescharacteristic
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1131no—
279C22⋊C4—1131no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C42—1131no—
286C42—1131no—
287C42—2261no—
288C42—2261no—
289C23—21no—
290C23—2261no—
291C23—2261no—
292C23D4×D11311yescharacteristic
293Q8—1132no—
294Q8—2261no—
295D4—21no—
296D4—21no—
297D4—81no—
298D4—1132no—
299D4—9041no—
300D4—9041no—
301D4—9041no—
302D4—2264no—
303D4—2261no—
304D4—2261no—
305D4—2261no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—1131no—
315C2×C4—1131no—
316C2×C4—9041no—
317C2×C4—9041no—
318C2×C4—9041no—
319C2×C4—9041no—
320C2×C4—2264no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4D4×D11311yescharacteristic
324C2×C4C23×D11311yescharacteristic
325C8—21no—
326C8—21no—
327C8—2261no—
328C8—2261no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—4521no—
336C22—4521no—
337C22—4521no—
338C22—4521no—
339C22—4521no—
340C22—2262no—
341C22C2×D4×D11311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—4521no—
347C4—2262no—
348C4—2261no—
349C4—2261no—
350C4—2261no—
351C4—2261no—
352C4#41×D11311yescharacteristic
353C4#41×D11311yescharacteristic
354C2—41no—
355C2—81no—
356C2—9041no—
357C2—4522no—
358C2#2029910611yescharacteristic
359C2#2029939911yescharacteristic
360C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#480×C113C2
socleC22×C113C22×D4
hypercenter#480D113
hypocenterC113#3119
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20299201C2semidirect
2. #20299079C2semidirect
3. #20298916C2semidirect
4. #20298904C2semidirect
5. #20298901C2semidirect
6. #20298797C2semidirect
7. #20298792C2semidirect
8. #20298745C2semidirect
9. #20298741C2semidirect
10. #20298707C2semidirect
11. #20298697C2semidirect
12. #20298689C2semidirect
13. #20298680C2semidirect
14. #20298656C2semidirect
15. #480×C113C2semidirect
181. C113#3119semidirect
185. #480D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202992012
#202990792
#202989162
#202989042
#202989012
#202987972
#202987922
#202987452
#202987412
#202987072
#202986972
#202986892
#202986802
#202986562
#480×C1132
#3119113